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    {
      "cell_type": "code",
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      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n",
        "# SVM Tie Breaking Example\n",
        "Tie breaking is costly if ``decision_function_shape='ovr'``, and therefore it\n",
        "is not enabled by default. This example illustrates the effect of the\n",
        "``break_ties`` parameter for a multiclass classification problem and\n",
        "``decision_function_shape='ovr'``.\n",
        "\n",
        "The two plots differ only in the area in the middle where the classes are\n",
        "tied. If ``break_ties=False``, all input in that area would be classified as\n",
        "one class, whereas if ``break_ties=True``, the tie-breaking mechanism will\n",
        "create a non-convex decision boundary in that area.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Automatically created module for IPython interactive environment\n"
          ]
        },
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "print(__doc__)\n",
        "\n",
        "\n",
        "# Code source: Andreas Mueller, Adrin Jalali\n",
        "# License: BSD 3 clause\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.svm import SVC\n",
        "from sklearn.datasets import make_blobs\n",
        "\n",
        "X, y = make_blobs(random_state=27)\n",
        "\n",
        "fig, sub = plt.subplots(2, 1, figsize=(5, 8))\n",
        "titles = (\"break_ties = False\",\n",
        "          \"break_ties = True\")\n",
        "\n",
        "for break_ties, title, ax in zip((False, True), titles, sub.flatten()):\n",
        "\n",
        "    svm = SVC(kernel=\"linear\", C=1, break_ties=break_ties,\n",
        "              decision_function_shape='ovr').fit(X, y)\n",
        "\n",
        "    xlim = [X[:, 0].min(), X[:, 0].max()]\n",
        "    ylim = [X[:, 1].min(), X[:, 1].max()]\n",
        "\n",
        "    xs = np.linspace(xlim[0], xlim[1], 1000)\n",
        "    ys = np.linspace(ylim[0], ylim[1], 1000)\n",
        "    xx, yy = np.meshgrid(xs, ys)\n",
        "\n",
        "    pred = svm.predict(np.c_[xx.ravel(), yy.ravel()])\n",
        "\n",
        "    colors = [plt.cm.Accent(i) for i in [0, 4, 7]]\n",
        "\n",
        "    points = ax.scatter(X[:, 0], X[:, 1], c=y, cmap=\"Accent\")\n",
        "    classes = [(0, 1), (0, 2), (1, 2)]\n",
        "    line = np.linspace(X[:, 1].min() - 5, X[:, 1].max() + 5)\n",
        "    ax.imshow(-pred.reshape(xx.shape), cmap=\"Accent\", alpha=.2,\n",
        "              extent=(xlim[0], xlim[1], ylim[1], ylim[0]))\n",
        "\n",
        "    for coef, intercept, col in zip(svm.coef_, svm.intercept_, classes):\n",
        "        line2 = -(line * coef[1] + intercept) / coef[0]\n",
        "        ax.plot(line2, line, \"-\", c=colors[col[0]])\n",
        "        ax.plot(line2, line, \"--\", c=colors[col[1]])\n",
        "    ax.set_xlim(xlim)\n",
        "    ax.set_ylim(ylim)\n",
        "    ax.set_title(title)\n",
        "    ax.set_aspect(\"equal\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "tags": [
          "outputPrepend"
        ]
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "809\n",
            "迭代轮次: 20518    e: 2.8015561818498713\n",
            "迭代轮次: 20519    e: 2.80155611200795\n",
            "迭代轮次: 20520    e: 2.801556042198027\n",
            "迭代轮次: 20521    e: 2.801555972420094\n",
            "迭代轮次: 20522    e: 2.8015559026741252\n",
            "迭代轮次: 20523    e: 2.8015558329601093\n",
            "迭代轮次: 20524    e: 2.8015557632780315\n",
            "迭代轮次: 20525    e: 2.8015556936278814\n",
            "迭代轮次: 20526    e: 2.8015556240096333\n",
            "迭代轮次: 20527    e: 2.801555554423278\n",
            "迭代轮次: 20528    e: 2.801555484868801\n",
            "迭代轮次: 20529    e: 2.8015554153461832\n",
            "迭代轮次: 20530    e: 2.80155534585541\n",
            "迭代轮次: 20531    e: 2.8015552763964693\n",
            "迭代轮次: 20532    e: 2.8015552069693457\n",
            "迭代轮次: 20533    e: 2.8015551375740206\n",
            "迭代轮次: 20534    e: 2.801555068210475\n",
            "迭代轮次: 20535    e: 2.8015549988786996\n",
            "迭代轮次: 20536    e: 2.8015549295786797\n",
            "迭代轮次: 20537    e: 2.8015548603103966\n",
            "迭代轮次: 20538    e: 2.801554791073837\n",
            "迭代轮次: 20539    e: 2.8015547218689814\n",
            "迭代轮次: 20540    e: 2.801554652695825\n",
            "迭代轮次: 20541    e: 2.801554583554341\n",
            "迭代轮次: 20542    e: 2.80155451444452\n",
            "迭代轮次: 20543    e: 2.8015544453663432\n",
            "迭代轮次: 20544    e: 2.801554376319797\n",
            "迭代轮次: 20545    e: 2.8015543073048677\n",
            "迭代轮次: 20546    e: 2.8015542383215397\n",
            "迭代轮次: 20547    e: 2.8015541693697954\n",
            "迭代轮次: 20548    e: 2.801554100449619\n",
            "迭代轮次: 20549    e: 2.8015540315609995\n",
            "迭代轮次: 20550    e: 2.801553962703922\n",
            "迭代轮次: 20551    e: 2.8015538938783666\n",
            "迭代轮次: 20552    e: 2.801553825084316\n",
            "迭代轮次: 20553    e: 2.8015537563217636\n",
            "迭代轮次: 20554    e: 2.8015536875906886\n",
            "迭代轮次: 20555    e: 2.801553618891075\n",
            "迭代轮次: 20556    e: 2.8015535502229088\n",
            "迭代轮次: 20557    e: 2.801553481586176\n",
            "迭代轮次: 20558    e: 2.8015534129808635\n",
            "迭代轮次: 20559    e: 2.8015533444069503\n",
            "迭代轮次: 20560    e: 2.801553275864424\n",
            "迭代轮次: 20561    e: 2.801553207353272\n",
            "迭代轮次: 20562    e: 2.801553138873477\n",
            "迭代轮次: 20563    e: 2.8015530704250238\n",
            "迭代轮次: 20564    e: 2.8015530020078967\n",
            "迭代轮次: 20565    e: 2.80155293362208\n",
            "迭代轮次: 20566    e: 2.8015528652675608\n",
            "迭代轮次: 20567    e: 2.801552796944321\n",
            "迭代轮次: 20568    e: 2.8015527286523496\n",
            "迭代轮次: 20569    e: 2.801552660391627\n",
            "迭代轮次: 20570    e: 2.801552592162144\n",
            "迭代轮次: 20571    e: 2.801552523963875\n",
            "迭代轮次: 20572    e: 2.8015524557968186\n",
            "迭代轮次: 20573    e: 2.8015523876609474\n",
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            "迭代轮次: 20865    e: 2.8015337652731027\n",
            "迭代轮次: 20866    e: 2.8015337056568868\n",
            "迭代轮次: 20867    e: 2.8015336460677323\n",
            "迭代轮次: 20868    e: 2.8015335865056246\n",
            "迭代轮次: 20869    e: 2.8015335269705566\n",
            "迭代轮次: 20870    e: 2.801533467462513\n",
            "迭代轮次: 20871    e: 2.8015334079814807\n",
            "迭代轮次: 20872    e: 2.8015333485274465\n",
            "迭代轮次: 20873    e: 2.801533289100398\n",
            "迭代轮次: 20874    e: 2.8015332297003184\n",
            "迭代轮次: 20875    e: 2.801533170327199\n",
            "迭代轮次: 20876    e: 2.8015331109810258\n",
            "迭代轮次: 20877    e: 2.801533051661787\n",
            "迭代轮次: 20878    e: 2.801532992369464\n",
            "迭代轮次: 20879    e: 2.801532933104053\n",
            "迭代轮次: 20880    e: 2.801532873865535\n",
            "迭代轮次: 20881    e: 2.801532814653896\n",
            "迭代轮次: 20882    e: 2.8015327554691276\n",
            "迭代轮次: 20883    e: 2.801532696311212\n",
            "迭代轮次: 20884    e: 2.801532637180138\n",
            "迭代轮次: 20885    e: 2.801532578075894\n",
            "迭代轮次: 20886    e: 2.801532518998469\n",
            "迭代轮次: 20887    e: 2.8015324599478446\n",
            "迭代轮次: 20888    e: 2.801532400924011\n",
            "迭代轮次: 20889    e: 2.8015323419269578\n",
            "迭代轮次: 20890    e: 2.8015322829566642\n",
            "迭代轮次: 20891    e: 2.801532224013125\n",
            "迭代轮次: 20892    e: 2.8015321650963276\n",
            "迭代轮次: 20893    e: 2.80153210620625\n",
            "迭代轮次: 20894    e: 2.8015320473428886\n",
            "迭代轮次: 20895    e: 2.8015319885062273\n",
            "迭代轮次: 20896    e: 2.8015319296962553\n",
            "迭代轮次: 20897    e: 2.8015318709129544\n",
            "迭代轮次: 20898    e: 2.801531812156319\n",
            "迭代轮次: 20899    e: 2.8015317534263278\n",
            "迭代轮次: 20900    e: 2.801531694722975\n",
            "迭代轮次: 20901    e: 2.801531636046245\n",
            "迭代轮次: 20902    e: 2.801531577396125\n",
            "迭代轮次: 20903    e: 2.801531518772602\n",
            "迭代轮次: 20904    e: 2.8015314601756636\n",
            "迭代轮次: 20905    e: 2.801531401605298\n",
            "迭代轮次: 20906    e: 2.801531343061492\n",
            "迭代轮次: 20907    e: 2.801531284544229\n",
            "迭代轮次: 20908    e: 2.8015312260535024\n",
            "迭代轮次: 20909    e: 2.801531167589294\n",
            "迭代轮次: 20910    e: 2.8015311091515946\n",
            "迭代轮次: 20911    e: 2.8015310507403894\n",
            "迭代轮次: 20912    e: 2.8015309923556666\n",
            "迭代轮次: 20913    e: 2.8015309339974146\n",
            "迭代轮次: 20914    e: 2.8015308756656183\n",
            "迭代轮次: 20915    e: 2.801530817360262\n",
            "迭代轮次: 20916    e: 2.8015307590813427\n",
            "迭代轮次: 20917    e: 2.8015307008288377\n",
            "迭代轮次: 20918    e: 2.80153064260274\n",
            "迭代轮次: 20919    e: 2.801530584403037\n",
            "迭代轮次: 20920    e: 2.801530526229712\n",
            "迭代轮次: 20921    e: 2.8015304680827566\n",
            "迭代轮次: 20922    e: 2.8015304099621545\n",
            "迭代轮次: 20923    e: 2.8015303518678953\n",
            "迭代轮次: 20924    e: 2.801530293799964\n",
            "迭代轮次: 20925    e: 2.801530235758349\n",
            "迭代轮次: 20926    e: 2.8015301777430404\n",
            "迭代轮次: 20927    e: 2.8015301197540228\n",
            "迭代轮次: 20928    e: 2.8015300617912815\n",
            "迭代轮次: 20929    e: 2.8015300038548085\n",
            "迭代轮次: 20930    e: 2.801529945944588\n",
            "迭代轮次: 20931    e: 2.8015298880606094\n",
            "迭代轮次: 20932    e: 2.8015298302028535\n",
            "迭代轮次: 20933    e: 2.801529772371319\n",
            "迭代轮次: 20934    e: 2.801529714565986\n",
            "迭代轮次: 20935    e: 2.8015296567868435\n",
            "迭代轮次: 20936    e: 2.801529599033876\n",
            "迭代轮次: 20937    e: 2.801529541307076\n",
            "迭代轮次: 20938    e: 2.8015294836064286\n",
            "迭代轮次: 20939    e: 2.8015294259319186\n",
            "迭代轮次: 20940    e: 2.8015293682835356\n",
            "迭代轮次: 20941    e: 2.8015293106612686\n",
            "迭代轮次: 20942    e: 2.8015292530651013\n",
            "迭代轮次: 20943    e: 2.8015291954950277\n",
            "迭代轮次: 20944    e: 2.8015291379510256\n",
            "迭代轮次: 20945    e: 2.8015290804330886\n",
            "迭代轮次: 20946    e: 2.8015290229412044\n",
            "迭代轮次: 20947    e: 2.801528965475363\n",
            "迭代轮次: 20948    e: 2.8015289080355434\n",
            "迭代轮次: 20949    e: 2.8015288506217364\n",
            "迭代轮次: 20950    e: 2.8015287932339348\n",
            "迭代轮次: 20951    e: 2.80152873587212\n",
            "迭代轮次: 20952    e: 2.801528678536285\n",
            "迭代轮次: 20953    e: 2.8015286212264114\n",
            "迭代轮次: 20954    e: 2.8015285639424876\n",
            "迭代轮次: 20955    e: 2.801528506684501\n",
            "迭代轮次: 20956    e: 2.8015284494524435\n",
            "迭代轮次: 20957    e: 2.8015283922462997\n",
            "迭代轮次: 20958    e: 2.8015283350660587\n",
            "迭代轮次: 20959    e: 2.801528277911705\n",
            "迭代轮次: 20960    e: 2.8015282207832253\n",
            "迭代轮次: 20961    e: 2.8015281636806137\n",
            "迭代轮次: 20962    e: 2.8015281066038518\n",
            "迭代轮次: 20963    e: 2.8015280495529304\n",
            "迭代轮次: 20964    e: 2.8015279925278302\n",
            "迭代轮次: 20965    e: 2.801527935528547\n",
            "迭代轮次: 20966    e: 2.801527878555066\n",
            "迭代轮次: 20967    e: 2.801527821607373\n",
            "迭代轮次: 20968    e: 2.8015277646854604\n",
            "迭代轮次: 20969    e: 2.80152770778931\n",
            "迭代轮次: 20970    e: 2.8015276509189095\n",
            "迭代轮次: 20971    e: 2.8015275940742517\n",
            "迭代轮次: 20972    e: 2.8015275372553177\n",
            "迭代轮次: 20973    e: 2.801527480462101\n",
            "迭代轮次: 20974    e: 2.801527423694587\n",
            "迭代轮次: 20975    e: 2.80152736695276\n",
            "迭代轮次: 20976    e: 2.801527310236613\n",
            "迭代轮次: 20977    e: 2.8015272535461286\n",
            "迭代轮次: 20978    e: 2.8015271968813\n",
            "迭代轮次: 20979    e: 2.8015271402421105\n",
            "迭代轮次: 20980    e: 2.80152708362855\n",
            "迭代轮次: 20981    e: 2.801527027040602\n",
            "迭代轮次: 20982    e: 2.8015269704782626\n",
            "迭代轮次: 20983    e: 2.8015269139415087\n",
            "迭代轮次: 20984    e: 2.8015268574303374\n",
            "迭代轮次: 20985    e: 2.801526800944733\n",
            "迭代轮次: 20986    e: 2.8015267444846796\n",
            "迭代轮次: 20987    e: 2.801526688050172\n",
            "迭代轮次: 20988    e: 2.8015266316411913\n",
            "迭代轮次: 20989    e: 2.801526575257727\n",
            "迭代轮次: 20990    e: 2.8015265188997645\n",
            "迭代轮次: 20991    e: 2.8015264625673\n",
            "迭代轮次: 20992    e: 2.8015264062603142\n",
            "迭代轮次: 20993    e: 2.8015263499787966\n",
            "迭代轮次: 20994    e: 2.801526293722735\n",
            "迭代轮次: 20995    e: 2.8015262374921153\n",
            "迭代轮次: 20996    e: 2.8015261812869303\n",
            "迭代轮次: 20997    e: 2.80152612510716\n",
            "迭代轮次: 20998    e: 2.8015260689527985\n",
            "迭代轮次: 20999    e: 2.801526012823831\n",
            "迭代轮次: 21000    e: 2.8015259567202464\n",
            "迭代轮次: 21001    e: 2.801525900642032\n",
            "迭代轮次: 21002    e: 2.8015258445891726\n",
            "迭代轮次: 21003    e: 2.801525788561662\n",
            "迭代轮次: 21004    e: 2.8015257325594827\n",
            "迭代轮次: 21005    e: 2.8015256765826275\n",
            "迭代轮次: 21006    e: 2.8015256206310784\n",
            "迭代轮次: 21007    e: 2.8015255647048294\n",
            "迭代轮次: 21008    e: 2.801525508803861\n",
            "迭代轮次: 21009    e: 2.8015254529281672\n",
            "迭代轮次: 21010    e: 2.801525397077729\n",
            "迭代轮次: 21011    e: 2.8015253412525447\n",
            "迭代轮次: 21012    e: 2.801525285452592\n",
            "迭代轮次: 21013    e: 2.8015252296778677\n",
            "迭代轮次: 21014    e: 2.801525173928351\n",
            "迭代轮次: 21015    e: 2.8015251182040357\n",
            "迭代轮次: 21016    e: 2.801525062504907\n",
            "迭代轮次: 21017    e: 2.8015250068309525\n",
            "迭代轮次: 21018    e: 2.8015249511821634\n",
            "迭代轮次: 21019    e: 2.8015248955585235\n",
            "迭代轮次: 21020    e: 2.8015248399600234\n",
            "迭代轮次: 21021    e: 2.8015247843866495\n",
            "迭代轮次: 21022    e: 2.8015247288383898\n",
            "迭代轮次: 21023    e: 2.801524673315233\n",
            "迭代轮次: 21024    e: 2.8015246178171638\n",
            "迭代轮次: 21025    e: 2.8015245623441776\n",
            "迭代轮次: 21026    e: 2.8015245068962535\n",
            "迭代轮次: 21027    e: 2.8015244514733855\n",
            "迭代轮次: 21028    e: 2.801524396075558\n",
            "迭代轮次: 21029    e: 2.8015243407027626\n",
            "迭代轮次: 21030    e: 2.801524285354984\n",
            "迭代轮次: 21031    e: 2.801524230032213\n",
            "迭代轮次: 21032    e: 2.8015241747344337\n",
            "迭代轮次: 21033    e: 2.8015241194616367\n",
            "迭代轮次: 21034    e: 2.801524064213809\n",
            "迭代轮次: 21035    e: 2.8015240089909406\n",
            "迭代轮次: 21036    e: 2.801523953793017\n",
            "迭代轮次: 21037    e: 2.8015238986200286\n",
            "迭代轮次: 21038    e: 2.8015238434719607\n",
            "迭代轮次: 21039    e: 2.8015237883488004\n",
            "迭代轮次: 21040    e: 2.8015237332505394\n",
            "迭代轮次: 21041    e: 2.801523678177165\n",
            "迭代轮次: 21042    e: 2.801523623128661\n",
            "迭代轮次: 21043    e: 2.8015235681050235\n",
            "迭代轮次: 21044    e: 2.8015235131062317\n",
            "迭代轮次: 21045    e: 2.801523458132279\n",
            "迭代轮次: 21046    e: 2.8015234031831517\n",
            "迭代轮次: 21047    e: 2.8015233482588378\n",
            "迭代轮次: 21048    e: 2.8015232933593284\n",
            "迭代轮次: 21049    e: 2.801523238484607\n",
            "迭代轮次: 21050    e: 2.801523183634665\n",
            "迭代轮次: 21051    e: 2.801523128809488\n",
            "迭代轮次: 21052    e: 2.801523074009064\n",
            "迭代轮次: 21053    e: 2.8015230192333838\n",
            "迭代轮次: 21054    e: 2.8015229644824324\n",
            "矩阵Q为：\n",
            " [[-0.79312959  0.83137956  2.16791912  2.29159838  1.33862441]\n",
            " [ 2.38077241  1.25671514  0.15786677  0.53916139  2.02803834]]\n",
            "矩阵P为：\n",
            " [[ 0.09216198  2.06869159]\n",
            " [ 0.10391407  1.78286882]\n",
            " [ 1.96404445  1.10827595]\n",
            " [ 1.93774358  1.07205767]\n",
            " [ 2.1601383  -0.88026594]\n",
            " [ 1.61096098  0.90901486]]\n",
            "矩阵R为：\n",
            " [[5 3 1 1 4]\n",
            " [4 0 0 1 4]\n",
            " [1 0 0 5 5]\n",
            " [1 3 0 5 0]\n",
            " [0 1 5 4 1]\n",
            " [1 2 3 5 4]]\n"
          ]
        },
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "name 'numpy' is not defined",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[1;32m<ipython-input-6-ee5f481cd14f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     62\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"矩阵P为：\\n\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mP\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     63\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"矩阵R为：\\n\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mR\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 64\u001b[1;33m \u001b[0mMF\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mQ\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     65\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"预测矩阵：\\n\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mMF\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     66\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;31mNameError\u001b[0m: name 'numpy' is not defined"
          ]
        }
      ],
      "source": [
        "import numpy as np  \n",
        "import matplotlib.pyplot as plt\n",
        " \n",
        " \n",
        "def matrix(R, P, Q, K, alpha, beta):\n",
        "    result=[]\n",
        "    steps = 1\n",
        "    while 1 :\n",
        "    #使用梯度下降的一步步的更新P,Q矩阵直至得到最终收敛值\n",
        "        steps = steps + 1    \n",
        "        eR = np.dot(P,Q)\n",
        "        e=0\n",
        "        for i in range(len(R)):\n",
        "            for j in range(len(R[i])):\n",
        "                if R[i][j]>0:\n",
        "                    # .dot(P,Q) 表示矩阵内积,即Pik和Qkj k由1到k的和eij为真实值和预测值的之间的误差,\n",
        "                    eij=R[i][j]-np.dot(P[i,:],Q[:,j]) \n",
        "                    #求误差函数值，我们在下面更新p和q矩阵的时候我们使用的是化简得到的最简式，较为简便，\n",
        "                    #但下面我们仍久求误差函数值这里e求的是每次迭代的误差函数值，用于绘制误差函数变化图\n",
        "                    e=e+pow(R[i][j] - np.dot(P[i,:],Q[:,j]),2) \n",
        "                    for k in range(K):\n",
        "                        #在上面的误差函数中加入正则化项防止过拟合\n",
        "                        e=e+(beta/2)*(pow(P[i][k],2)+pow(Q[k][j],2))\n",
        "                        \n",
        "                    for k in range(K):\n",
        "                        #在更新p,q时我们使用化简得到了最简公式\n",
        "                        P[i][k]=P[i][k]+alpha*(2*eij*Q[k][j]-beta*P[i][k])\n",
        "                        Q[k][j]=Q[k][j]+alpha*(2*eij*P[i][k]-beta*Q[k][j])\n",
        "        # print('迭代轮次:', steps, '   e:', e)\n",
        "        result.append(e)#将每一轮更新的损失函数值添加到数组result末尾\n",
        "        \n",
        "        #当损失函数小于一定值时，迭代结束\n",
        "        if eij<0.00001:\n",
        "            break\n",
        "    return P,Q,result\n",
        " \n",
        " \n",
        "    \n",
        "R=[\n",
        "   [5,3,1,1,4],\n",
        "   [4,0,0,1,4],\n",
        "   [1,0,0,5,5],\n",
        "   [1,3,0,5,0],\n",
        "   [0,1,5,4,1],\n",
        "   [1,2,3,5,4]\n",
        "   ]\n",
        " \n",
        "R=np.array(R)\n",
        "    \n",
        "alpha = 0.0001 #学习率\n",
        "beta = 0.002 #\n",
        " \n",
        "N = len(R)\n",
        "M = len(R[0])\n",
        "K = 2\n",
        " \n",
        "p = np.random.rand(N, K) #随机生成一个 N行 K列的矩阵\n",
        "q = np.random.rand(K, M) #随机生成一个 M行 K列的矩阵\n",
        " \n",
        "P, Q, result=matrix(R, p, q, K,  alpha, beta)\n",
        "print(\"矩阵Q为：\\n\",Q)\n",
        "print(\"矩阵P为：\\n\",P)\n",
        "print(\"矩阵R为：\\n\",R)\n",
        "MF = numpy.dot(P,Q)\n",
        "print(\"预测矩阵：\\n\",MF)\n",
        " \n",
        " \n",
        "#下面代码可以绘制损失函数的收敛曲线图\n",
        "n=len(result)\n",
        "x=range(n)\n",
        "plt.plot(x, result,color='b',linewidth=3)\n",
        "plt.xlabel(\"generation\")\n",
        "plt.ylabel(\"loss\")\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
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